Strategic Approaches for CAT Success: Ranking & Derrangements, One-word Substitution - Day 38

Part-1: Quantitative Aptitude for CAT exam

CAT Exam Important Topic: Strategy to Prepare “Permutations and Combinations (Ranking and Derangements)” and ranking arrangement questions

Important Concept/Formula Used in Derangement

Problems on Derangement and Ranking

1. Finding of Rank of a word in a dictionary with no alphabet is repeating: See link in references
2. Finding the Rank of a word (if letters are repeating): See link in references
3. Concept of Derangements: permutation of the elements of a certain set in a way that no element of that set appears in their original positions.
4. The number of derangements of a set with n objects is given by the formula

CAT Exam: Previous Year CAT Questions On Permutations and Combinations (Ranking and Derangements)

Q1. All the rearrangements of the word "DEMAND" are written without including any word that has two D's appearing together. If these are arranged alphabetically, what would be the rank of "DEMAND"? [CAT PYQ]

A. 36 B. 74 C. 42 D. 86

Ranking Arrangement Questions With Answers: (B)

Total words formed from the word DEMAND = 6! /2! = 360

Total words formed from the word DEMAND where 2 D’s appear together = 5! = 120

Total words formed from the word DEMAND where 2D’s do not appear together =

360 – 120 = 240

Words starting with ‘A’, without two D’s adjacent to each = Words starting with A - Words starting with A where 2 D’s are together

⇒ Words starting with ‘A’, without two D’s adjacent to each = 5!/2! - 4! = 36.

Next letter is D (in alphabetical order from the letters of the word DEMAND)

Words starting with DA: 4! words = 24 words

Words starting with DEA = 3! = 6 words

Words starting with DEA = 3! = 6 words

Words starting with DEMA

=> First word is DEMADN

=> Second is DEMAND

Rank of DEMAND = 36 + 24 + 6 + 6 + 2 = 74

Derangement and Ranking

Q2. In how many ways can you put 6 letters into their respective envelopes such that exactly 4 go into the right envelope? [CAT Sample Question]

a) 24 b) 102 c)15 d) 530

Ranking Arrangement Questions With Answers: (C)

No of ways in which the 4 correct envelopes can be selected= ⁶C₄ =15

Derangement of the remaining 2 envelopes & letters =

= 2! (1 -1 + ½) = 1

Total No of ways of arrangement = 1 x 15= 15.

CAT entrance exam: Prerequisite to Derangement

1. Factorial

2. Fundamental Principle of counting,

3. Concept of Selection and Arrangement

Tips and Tricks of Ranking Arrangement Questions for CAT

1. For ⁿC_r to be greatest,

   • if n is even, r = n/2
   • if n is odd, r = (n + 1)/2 or (n – 1)/2

2. Number of squares in a square of n × n side = 1² + 2² + 3² + 4² + … n²

3. Number of rectangles in a square of n × n side = 1³ + 2³ +3³ + 4³ + … n³. (This includes the number of squares.)

4. Practice sample papers and questions based on previous years CAT Questions.

5. Do not spend much time on this.

CAT study material: References to Study (Theory) Derangement and Ranking

1. NCERT Class 11 Maths
2. Concept Tree (YouTube, Link: https://www.youtube.com/watch?v=A4Fp-vP243k)
3. CAT Funda (YouTube, Link: https://www.youtube.com/watch?v=QCqj1ijqp8w)

CAT study material: References to Practice ranking arrangement questions

1. How to prepare quantitative Aptitude for CAT by Arun Sharma.
2. (CAT PYQs https://www.youtube.com/watch?v=P0UQxxR_slc)

Part-2: CAT 2023 Preparation Tips: CAT DILR tips (Logical Reasoning and Data Interpretation)

CAT 2023 Syllabus Topic: Strategy to prepare “Logical Deduction” for CAT

Important Concepts/ Formulas used in Logical Deduction

Middle term: It is the term common to both the premise and is denoted by ‘M’.

Major premise: The premise in which the middle term is in place of the predicate is called a major premise.

Minor premise: The premise in which the middle term is in the place of the subject is called a minor premise.

Subject vs Predicate: Consider this question statement

1. All cats are dogs
2. Some dogs are birds
3. No bird is a pig
4. Some pigs are not birds.

In all such statements, the first term is called the subject and the second is called the predicate.

CAT Exam: Previous years Questions on Logical Deduction from CAT/ MBA Entrance Exam:

Q1. Statements: No Arc is Circle. Some Arc are Triangles.

Conclusions:

Square are Circles

Some Triangles are Circles.

1. The only conclusion I follow

2. Only conclusion II follows

3. Either I or II follows

4. Neither I nor II follows

5. Both I and II follow

Solution: [D]

Statement I is negative.

Statemnet II is negative.

Therefore Negative conclusion must be there.

But neither conclusion is negative.

Logical Deduction Questions

Q2. The question contains six statements, followed by four options of combinations of any three of the given sentences. Choose the option in which the combinations are logically related. Consider the first two as statements and the third as conclusions:

Statements:

1. Some pinks are colour.
2. No Blue is black.

Conclusions:

1. All pink are spark.
2. Some sparks are not E.
3. Some yellow are black.
4. Some pink are black.

1. ABD 2. ABF 3. CDE 4. BCF 5. NOT

Solution: (5)

We must check option (1) only (rest are false); No common term is there A and B, so no conclusion can be drawn.

Hence answer is (5)

CAT entrance exam: Prerequisite

1. Syllogism
2. Venn Diagram

Tips and Tricks for CAT Logical Deduction Questions

1. There should be three and only three distinct terms between two premises for the conclusion to be obtained.

2. The middle term should be distributed at least once on the premises for the conclusion to be obtained.

4. Learn the rule of distribution (See References to Study Link)

5. Practice Sample Papers.

References to CAT Study (Theory) Logical Deduction

1. LRDI by Nikhil K. Sinha
2. Concept Tree (YouTube link: https://www.youtube.com/watch?v=lkyRADOwUuY)
3. (YouTube link: https://www.youtube.com/watch?v=lsl5y8xlqCw&t=442s)

References to Practice Logical Deduction questions

1. Verbal and Non-Verbal Reasoning by R S Agrawal.
2. MBA Entrance Previous years Papers and Sample Papers.

Part-3: CAT Exam Preparation 2023: CAT exam tips for VARC (Verbal Ability & Reading Comprehension)

CAT Exam Important Topic: Strategy to Prepare “One Word Substitution” and one word substitution questions for competitive exams such as CAT-2023

CAT Tips and Tricks for One Word Substitution Questions:

1. Divide the One-word substitutions into the categories like

One Word Substitution for Study

Some Examples:

Words used for people with various qualities, habits, and abilities.

Some Examples:

Words for likes and dislikes

Some Examples:

Words used for practices & beliefs

Some Examples:

Words used for various kinds of killings

Some Examples:

There can be more categories like this.

2. Remember the following factors while choosing a word for a sentence

• Contextual
• Grammatical
• Tone of sentence
• Insight

3. Learning more about substitution will be helpful.

4. Practice Sample questions.

CAT Previous Years' Questions on One Word Substitution MCQs

Sample Questions:

Directions: Choose the best substitute from the given options for highlighted phrase

Q.1. We visited the ancient palace yesterday, there we saw old manuscripts written by saints, we tried but it was not clear enough to be read.

1. Corrigible
2. Legible
3. Negligible
4. Illegible

Ans: [4]

One word substitution quiz with answers

Q.2. They organized a house party for Sara’s birthday but she does not get excited easily even if you put in a lot of effort and emotion.

1. Gregarious
2. Placid
3. Inclement
4. Frenzied

Ans: [2]

CAT 2023: Prerequisite to one word substitution MCQs

1. Sentence Structure
2. Vocabulary
3. Parts of Speech

CAT exam: References to Study (Theory)

1. One word substitution questions for competitive exams
2. Wren and Martin
3. (https://www.youtube.com/watch?v=3YPMi1RbSb0)

CAT exam: References to Practice one word substitution questions

1. one-word substitution MCQs
2. Verbal Ability for CAT by Arun Sharma and Meenakshi Upadhyay.
3. CAT Previous years Papers and other MBA Entrance Exams.
4. (youTube; Link: https://www.youtube.com/watch?v=1DU9ZWbGvLs)

Practice and remain focused, and we'll be back tomorrow with Day 39.

Thank you! All the best!